**Work:**In our daily life anything that makes us tired is known as work. For example, reading, writing, painting, walking, etc.

In physics work (W) is said to be done, when a force (F) acts on the body and point of application of the force is displaced (s) in the direction of force.

Work done = force x displacement

W = F x s

(i) If the body is displaced in the same direction of force, Work done is positive

(ii) If the displacement is against a force, the work is done against the force. Work done is negative

(iii) If the displacement is perpendicular to the direction of the force, work done is zero.

Unit of work

Unit of work is joule (J). One joule of work is said to be done when a force of 1 Newton acting on a body displacing it by a distance of 1 m.

Larger units of work are

i) kilo joules (1000 joule) ii) mega joule (10 lakh joule)

ENERGY - The energy of the body is defined as its capacity to do work

Unit of energy - Energy is measured in terms of work. Unit of energy is also joule. One joule of energy is required to do one joule of work

__Different forms of energy__

1. Mechanical Energy

The energy used to displace a body or to change the position of the body or to deform the body is known as mechanical energy.

Mechanical energy is of two types i) Potential energy ii) Kinetic energy.

POTENTIAL ENERGY

The energy possessed by a body by virtue of its position or due to state of strain, is called potential energy.

Example :The work done to lift a body above the ground level gives the potential energy of the body. Eg. Weight lifting.

Water stored in reservoir has large amount of potential energy due to which it can drive a water turbine when allowed to fall down. This is the principle of production of hydro electric energy.

Expression for potential energy of a body above the ground level

By applying force F, The object gains energy to do the work done (w) on it.

Work done = force x displacement

w = F x h (Since F= m a , a = g , F = mg)

w = m g h

KINETIC ENERGY- Energy possessed by an object due to its motion is called kinetic energy.

Kinetic energy of an object increases with its speed. Kinetic energy of an object moving with a velocity is equal to the work done on it to make it acquire that velocity

Example - Kinetic energy of a hammer is used to drive a nail into the wall. Bullet fi red from a gun can penetrate into a target due to its kinetic energy.

Let a body (ball) of mass m is moving with an initial velocity v. If it is brought to rest by applying a retarding (opposing) force F, then it comes to rest by a displacement S.Let,

E

_{k}= work done against the force used to stop it.E

_{k}= F x S ---- (1)But retarding force F = ma-----(2)

Let initial velocity u = v, final velocity v = 0

From III equation of motion

v

^{2}= u^{2}+ 2aSApplying, 0 = v

^{2}– 2aS ( a is retardation)2aS = v2

Displacement, S = v

^{2}/2a ----> (3)Substituting (2) and (3) in (1)

E

E

_{k}= ma x v^{2}/2aE

_{k}= 1/2 mv^{2}Energy can neither be created nor destroyed, but it is transformed from one form to another. Alternatively, whenever energy gets transformed, the total energy remains unchanged.

Proof – Freely falling body

Consider a body of mass m falls from a point A, which is at a height h from the ground as shown in fig.

At A,

Kinetic energy E

_{k}= 0Potential energy E

_{p}= mghTotal energy E = E

_{p}+ E_{k} = mgh + 0

E = mgh

During the fall, the body is at a position B. The body has moved a distance x from A.

At B,

Velocity v

^{2}= u^{2}+ 2asApplying, v

^{2}= 0 + 2ax = 2axE

_{k}= 1/2 mv^{2} =1/2 m x 2gx

= mgx

Potential energy

E p = mg (h – x)

Total energy E = E

_{p}+ E_{k} = mg (h-x) + mgx

= mgh – mgx + mgx

E = mgh

If the body reaches the position C.

At C,

Potential energy E

Potential energy E

_{p}= 0Velocity of the body C is v

^{2}= u^{2}+ 2asu = 0, a = g, s = h

Applying v

^{2}= 0 + 2gh = 2ghKinetic energy Ek = 1/2 mv

^{2}= 1/2x m x 2gh E_{k}= mghTotal energy at C

E = E

_{p}+ E_{k} E = 0 + m g h

E = m g h

Thus sum of potential and kinetic energy of freely falling body at all points remains same.

Power : Power is defined as the rate of doing work or work done per unit time

Power = work done/time taken

P = w / t

UNIT OF POWER

The unit of power is J/S known as watt, its symbol is W.

1 watt = 1 joule/1 second

1 W = 1 J S

^{-1}1 kilowatt = 1000 watts

1 kW = 1000 W

1 kW = 1000 J /s.

^{}Commercial unit of energy is kilo watt hour

Example 1. How much energy will be used when a hundred watt bulb is used for 10 hour?

Energy = 100 watt x 10 hour

= 1000 w h = 1kw h

I k w h is known as 1 unit.

One kilowatt hour means thousand watt of power is consumed in one hour.

1 kWh = 1 kW x 1 h

= 1000 W x 60 x 60 s

= 1000 Js

^{-1}x 3600 s = 3.6 x 10

^{6}J1 unit = 1 kilowatt hour = 3.6x10

^{6}JExample 1: An electric bulb of 60 W is used for 6 h per day. Calculate the ‘units’ of energy consumed in one day by the bulb.

Solution: Power of electric bulb = 60 W = 0.06 kW. Time used,

*t*= 6 hEnergy = power × time taken = 0.06 kW × 6 h = 0.36 kW h = 0.36 ‘units’.

The energy consumed by the bulb is 0.36 ‘units’.

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